Factor analysis

0.1 Basic factor analysis: 7 factors as the number of variables in the study design

0.2 Read in data

all <- read.csv("../02-descriptive_data/merged_filtered_imputedMedian_likertNumber.csv")
rownames(all) <- all$Resp.ID

Seven, is the number of factors that would be present according to the study design. Using very relaxed cutoff of 0.2 to get rid of not important variables in each factor.

0.2.1 Likert variables

0.2.2 Delete some items which are context specific

# items to be used for the FA
usable_items <- likert_variables1[!(likert_variables1 %in% c("necessity1","educated1","reconnect.comm1", "speakersmelb.comm1", "comecloser.comm1"))]
usable_data <- all[,usable_items]
sum(is.na(usable_data))

[1] 0

# Cronbach's alpha using consistent items across contexts
psych::alpha(usable_data,use="pairwise.complete.obs")

Reliability analysis   
Call: psych::alpha(x = usable_data, use = "pairwise.complete.obs")

  raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd
      0.84      0.86     0.9      0.17 5.9 0.013    4 0.33

 lower alpha upper     95% confidence boundaries
0.81 0.84 0.86 

 Reliability if an item is dropped:
                   raw_alpha std.alpha G6(smc) average_r S/N alpha se
converse.id1            0.83      0.85    0.89      0.16 5.5    0.014
dream.id1               0.83      0.85    0.90      0.17 5.6    0.013
usewell.id1             0.83      0.85    0.90      0.17 5.7    0.013
whenever.id1            0.83      0.85    0.89      0.16 5.5    0.014
consider.ought1         0.84      0.86    0.90      0.18 6.0    0.012
people.ought1           0.84      0.86    0.90      0.17 5.9    0.013
expect.ought1           0.84      0.86    0.90      0.18 6.0    0.013
fail.ought1             0.84      0.86    0.90      0.18 6.0    0.013
enjoy.intr1             0.83      0.85    0.89      0.17 5.7    0.013
life.intr1              0.83      0.85    0.89      0.16 5.5    0.014
exciting.intr1          0.83      0.85    0.89      0.17 5.6    0.013
challenge.intr1         0.83      0.85    0.90      0.17 5.7    0.013
job.instru1             0.83      0.85    0.89      0.17 5.6    0.014
knowledge.instru1       0.83      0.85    0.90      0.17 5.8    0.013
career.instru1          0.83      0.85    0.89      0.17 5.6    0.014
money.instru1           0.83      0.85    0.90      0.17 5.8    0.013
time.integr1            0.83      0.85    0.89      0.17 5.6    0.013
becomelike.integr1      0.83      0.85    0.90      0.17 5.8    0.013
meeting.integr1         0.83      0.85    0.90      0.17 5.7    0.013
affinity.integr1        0.84      0.85    0.90      0.17 5.8    0.013
improve.prof1           0.83      0.85    0.90      0.17 5.7    0.013
speaking.prof1          0.83      0.85    0.89      0.17 5.6    0.013
reading.prof1           0.84      0.85    0.89      0.17 5.8    0.013
written.prof1           0.83      0.85    0.89      0.17 5.6    0.013
listening.prof1         0.83      0.85    0.89      0.17 5.6    0.013
citizen.post1           0.83      0.85    0.90      0.17 5.7    0.014
interact.post1          0.83      0.85    0.90      0.17 5.7    0.013
overseas.post1          0.83      0.85    0.89      0.17 5.6    0.014
globalaccess.post1      0.83      0.85    0.89      0.17 5.5    0.014

 Item statistics 
                     n raw.r std.r r.cor r.drop mean   sd
converse.id1       323  0.59  0.59  0.58   0.53  4.3 0.76
dream.id1          323  0.49  0.51  0.49   0.44  4.5 0.65
usewell.id1        323  0.42  0.43  0.40   0.35  4.3 0.72
whenever.id1       323  0.57  0.57  0.56   0.51  4.3 0.82
consider.ought1    323  0.27  0.20  0.16   0.16  2.6 1.12
people.ought1      323  0.36  0.28  0.24   0.25  3.1 1.16
expect.ought1      323  0.29  0.21  0.18   0.20  1.9 0.92
fail.ought1        323  0.29  0.23  0.19   0.20  2.1 0.96
enjoy.intr1        323  0.43  0.46  0.44   0.38  4.5 0.64
life.intr1         323  0.62  0.60  0.59   0.55  3.3 1.04
exciting.intr1     323  0.50  0.54  0.52   0.45  4.6 0.56
challenge.intr1    323  0.41  0.42  0.39   0.33  4.2 0.79
job.instru1        323  0.50  0.49  0.47   0.43  3.8 0.83
knowledge.instru1  323  0.39  0.40  0.36   0.33  4.2 0.65
career.instru1     323  0.50  0.50  0.49   0.43  4.2 0.77
money.instru1      323  0.40  0.39  0.36   0.33  3.2 0.77
time.integr1       323  0.46  0.49  0.46   0.40  4.5 0.66
becomelike.integr1 323  0.43  0.40  0.36   0.34  3.1 0.95
meeting.integr1    323  0.42  0.45  0.43   0.37  4.6 0.57
affinity.integr1   323  0.39  0.37  0.34   0.31  3.6 0.87
improve.prof1      323  0.38  0.43  0.41   0.32  4.5 0.75
speaking.prof1     323  0.44  0.50  0.50   0.40  4.7 0.53
reading.prof1      323  0.34  0.39  0.37   0.28  4.5 0.62
written.prof1      323  0.46  0.51  0.50   0.41  4.6 0.58
listening.prof1    323  0.44  0.49  0.49   0.39  4.5 0.63
citizen.post1      323  0.50  0.48  0.45   0.42  3.8 0.89
interact.post1     323  0.44  0.47  0.44   0.38  4.4 0.62
overseas.post1     323  0.51  0.55  0.53   0.47  4.6 0.58
globalaccess.post1 323  0.53  0.56  0.54   0.48  4.3 0.67

Non missing response frequency for each item
                      1    2    3    4    5 miss
converse.id1       0.00 0.03 0.10 0.41 0.47    0
dream.id1          0.00 0.00 0.07 0.36 0.56    0
usewell.id1        0.00 0.02 0.11 0.46 0.42    0
whenever.id1       0.00 0.03 0.12 0.37 0.47    0
consider.ought1    0.14 0.40 0.21 0.19 0.06    0
people.ought1      0.09 0.27 0.25 0.28 0.11    0
expect.ought1      0.39 0.44 0.09 0.07 0.01    0
fail.ought1        0.27 0.46 0.16 0.10 0.01    0
enjoy.intr1        0.00 0.01 0.06 0.40 0.54    0
life.intr1         0.02 0.24 0.25 0.36 0.12    0
exciting.intr1     0.00 0.01 0.02 0.37 0.61    0
challenge.intr1    0.00 0.03 0.12 0.48 0.36    0
job.instru1        0.00 0.04 0.32 0.41 0.23    0
knowledge.instru1  0.00 0.01 0.09 0.59 0.32    0
career.instru1     0.00 0.00 0.20 0.41 0.39    0
money.instru1      0.01 0.12 0.55 0.26 0.06    0
time.integr1       0.00 0.01 0.07 0.29 0.63    0
becomelike.integr1 0.03 0.23 0.47 0.18 0.10    0
meeting.integr1    0.00 0.00 0.03 0.37 0.59    0
affinity.integr1   0.01 0.07 0.36 0.39 0.17    0
improve.prof1      0.01 0.02 0.03 0.34 0.59    0
speaking.prof1     0.00 0.01 0.00 0.28 0.71    0
reading.prof1      0.00 0.02 0.02 0.38 0.59    0
written.prof1      0.00 0.01 0.02 0.36 0.62    0
listening.prof1    0.00 0.01 0.04 0.38 0.57    0
citizen.post1      0.01 0.07 0.23 0.46 0.23    0
interact.post1     0.00 0.00 0.06 0.43 0.50    0
overseas.post1     0.00 0.01 0.02 0.34 0.63    0
globalaccess.post1 0.00 0.01 0.06 0.49 0.43    0

fact <- 7
loading_cutoff <- 0.2
fa_basic <- fa(usable_data,fact)

Loading required namespace: GPArotation

fa_basic

Factor Analysis using method =  minres
Call: fa(r = usable_data, nfactors = fact)
Standardized loadings (pattern matrix) based upon correlation matrix
                     MR2   MR3   MR4   MR7   MR5   MR6   MR1   h2   u2
converse.id1        0.09  0.10  0.04  0.35  0.14  0.26  0.08 0.40 0.60
dream.id1           0.17  0.07  0.16  0.19  0.17 -0.04  0.38 0.39 0.61
usewell.id1        -0.02  0.03  0.18  0.13  0.17  0.06  0.30 0.28 0.72
whenever.id1       -0.03  0.12  0.18  0.11  0.28  0.21  0.25 0.44 0.56
consider.ought1     0.10  0.51  0.06  0.14 -0.09 -0.13 -0.18 0.38 0.62
people.ought1      -0.04  0.48  0.24  0.09  0.01 -0.14  0.08 0.31 0.69
expect.ought1       0.03  0.80  0.01  0.04 -0.03 -0.09 -0.06 0.68 0.32
fail.ought1        -0.02  0.73 -0.10 -0.12 -0.01  0.16  0.12 0.53 0.47
enjoy.intr1         0.02 -0.12  0.01  0.01  0.81 -0.06  0.01 0.66 0.34
life.intr1         -0.11  0.20  0.09  0.14  0.55  0.18  0.00 0.55 0.45
exciting.intr1      0.25  0.02 -0.02  0.16  0.33  0.07  0.14 0.35 0.65
challenge.intr1     0.21  0.00 -0.05 -0.03  0.45  0.07 -0.14 0.29 0.71
job.instru1         0.00  0.01  0.83  0.00 -0.03  0.01 -0.03 0.68 0.32
knowledge.instru1   0.12  0.13 -0.02 -0.02  0.15  0.33 -0.22 0.24 0.76
career.instru1      0.00 -0.06  0.65 -0.01  0.03  0.12  0.14 0.57 0.43
money.instru1       0.02  0.03  0.59 -0.08  0.08  0.02 -0.13 0.36 0.64
time.integr1        0.06 -0.05 -0.08  0.57  0.06  0.12  0.19 0.46 0.54
becomelike.integr1  0.01  0.05  0.03  0.49  0.12  0.04 -0.30 0.37 0.63
meeting.integr1     0.05 -0.11 -0.01  0.51  0.11  0.04  0.17 0.40 0.60
affinity.integr1   -0.09  0.04  0.01  0.74 -0.03 -0.04 -0.06 0.52 0.48
improve.prof1       0.70 -0.03 -0.07  0.08 -0.04  0.07 -0.06 0.51 0.49
speaking.prof1      0.80 -0.06  0.08  0.09 -0.10  0.00  0.01 0.65 0.35
reading.prof1       0.69  0.01 -0.03 -0.13  0.11 -0.04  0.01 0.51 0.49
written.prof1       0.76  0.05  0.08 -0.03  0.05 -0.06  0.09 0.61 0.39
listening.prof1     0.85  0.05 -0.06 -0.05  0.03  0.05 -0.05 0.76 0.24
citizen.post1       0.04  0.11  0.16  0.03  0.04  0.49 -0.28 0.42 0.58
interact.post1     -0.02 -0.12  0.16  0.05  0.10  0.40  0.13 0.36 0.64
overseas.post1      0.26 -0.02  0.10  0.12 -0.11  0.46  0.06 0.41 0.59
globalaccess.post1  0.00 -0.11  0.15  0.05  0.05  0.62  0.05 0.57 0.43
                   com
converse.id1       2.7
dream.id1          3.0
usewell.id1        3.0
whenever.id1       4.5
consider.ought1    1.8
people.ought1      1.8
expect.ought1      1.0
fail.ought1        1.3
enjoy.intr1        1.1
life.intr1         1.8
exciting.intr1     2.9
challenge.intr1    1.7
job.instru1        1.0
knowledge.instru1  3.0
career.instru1     1.2
money.instru1      1.2
time.integr1       1.4
becomelike.integr1 1.8
meeting.integr1    1.5
affinity.integr1   1.1
improve.prof1      1.1
speaking.prof1     1.1
reading.prof1      1.1
written.prof1      1.1
listening.prof1    1.0
citizen.post1      2.0
interact.post1     2.0
overseas.post1     2.0
globalaccess.post1 1.2

                       MR2  MR3  MR4  MR7  MR5  MR6  MR1
SS loadings           3.30 1.86 2.00 1.95 1.89 1.79 0.85
Proportion Var        0.11 0.06 0.07 0.07 0.07 0.06 0.03
Cumulative Var        0.11 0.18 0.25 0.31 0.38 0.44 0.47
Proportion Explained  0.24 0.14 0.15 0.14 0.14 0.13 0.06
Cumulative Proportion 0.24 0.38 0.53 0.67 0.81 0.94 1.00

 With factor correlations of 
     MR2   MR3  MR4  MR7   MR5  MR6   MR1
MR2 1.00  0.08 0.10 0.08  0.20 0.24  0.04
MR3 0.08  1.00 0.07 0.08 -0.03 0.02 -0.15
MR4 0.10  0.07 1.00 0.26  0.27 0.42  0.14
MR7 0.08  0.08 0.26 1.00  0.33 0.28  0.12
MR5 0.20 -0.03 0.27 0.33  1.00 0.36  0.20
MR6 0.24  0.02 0.42 0.28  0.36 1.00  0.14
MR1 0.04 -0.15 0.14 0.12  0.20 0.14  1.00

Mean item complexity =  1.8
Test of the hypothesis that 7 factors are sufficient.

The degrees of freedom for the null model are  406  and the objective function was  10.52 with Chi Square of  3278.37
The degrees of freedom for the model are 224  and the objective function was  1.23 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic number of observations is  323 with the empirical chi square  224.23  with prob <  0.48 
The total number of observations was  323  with Likelihood Chi Square =  376.07  with prob <  8.2e-10 

Tucker Lewis Index of factoring reliability =  0.902
RMSEA index =  0.049  and the 90 % confidence intervals are  0.038 0.054
BIC =  -918.12
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   MR2  MR3  MR4  MR7
Correlation of (regression) scores with factors   0.95 0.90 0.90 0.88
Multiple R square of scores with factors          0.90 0.81 0.82 0.77
Minimum correlation of possible factor scores     0.80 0.62 0.63 0.53
                                                   MR5  MR6  MR1
Correlation of (regression) scores with factors   0.89 0.86 0.75
Multiple R square of scores with factors          0.79 0.74 0.57
Minimum correlation of possible factor scores     0.58 0.49 0.13

# plot loadings
loadings_basic <- fa_basic$loadings
class(loadings_basic)<-"matrix"
colnames(loadings_basic)<-paste("F",1:fact,sep="")
loadings_basic<-as.data.frame(loadings_basic)
loadings_basic<-round(loadings_basic,2)
loadings_basic$D <- rownames(loadings_basic)
a1 <- loadings_basic
a1 <- melt(a1,id.vars=c("D"))
a1$inv <- ifelse(a1$value < 0 ,"neg","pos")
a1$value[abs(a1$value) < loading_cutoff] <- 0
a1 <- a1[a1$value!=0,]
a1 <- a1 %>% separate(D,into = c("Variable","Item"),remove=FALSE,sep="[.]")
ggplot(a1)+geom_bar(aes(x=reorder(D, value) ,y=value,fill=Item),stat="identity")+facet_wrap(~variable,ncol = 2,scales = "free_y")+coord_flip() + geom_hline(yintercept = c(-0.3,0.3),linetype="dotted",colour="dark red")

# Table of the factors
loadings_basic$D <- NULL
loadings_basic[abs(loadings_basic) < loading_cutoff] <- 0
for(i in 1:ncol(loadings_basic)){loadings_basic[,i] <- as.character(loadings_basic[,i])}
loadings_basic[loadings_basic=="0"] <- ""
loading_fact_reduced <- loadings_basic
loading_fact_reduced

# predict values per samples
pred_basic <- as.data.frame(predict(fa_basic,usable_data))
names(pred_basic) <- paste("Factor",1:fact,sep = "")
factors <- names(pred_basic)
match_initial_data <- match(all$Resp.ID,rownames(pred_basic))
all_complete_basic <- cbind(all,scale(pred_basic[match_initial_data,]))
corrplot(cor(all_complete_basic[,usable_items],all_complete_basic[,factors],use = "pair"))

# Plot loadings by context
all_complete_basic <- melt(all_complete_basic,id.vars = "Context",measure.vars = factors)
library(ggplot2)
ggplot(all_complete_basic)+geom_boxplot(aes(x=Context,y=value,color=Context))+facet_wrap(~variable)+coord_flip()+guides(color=F)

# 7 * 12 rows removed

0.3 Basic factor analysis: 6 factors

Using very relaxed cutoff of 0.2 to get rid of not important variables in each factor.

# items to be used for the FA
usable_items <- likert_variables1[!(likert_variables1 %in% c("necessity1","educated1","reconnect.comm1", "speakersmelb.comm1", "comecloser.comm1"))]
usable_data <- all[,usable_items]
# From a statisticak point of view 
fap <- fa.parallel(usable_data)

Parallel analysis suggests that the number of factors =  6  and the number of components =  4 

fact <- 6
loading_cutoff <- 0.2
fa_basic <- fa(usable_data,fact)
fa_basic

Factor Analysis using method =  minres
Call: fa(r = usable_data, nfactors = fact)
Standardized loadings (pattern matrix) based upon correlation matrix
                     MR2   MR4   MR3   MR5   MR1   MR6   h2   u2 com
converse.id1        0.10  0.12  0.06  0.38  0.20  0.13 0.40 0.60 2.3
dream.id1           0.18  0.27  0.04  0.22  0.25 -0.27 0.37 0.63 4.7
usewell.id1        -0.01  0.29 -0.01  0.16  0.25 -0.15 0.27 0.73 3.2
whenever.id1       -0.01  0.31  0.06  0.14  0.39 -0.01 0.43 0.57 2.3
consider.ought1     0.08 -0.04  0.57  0.10 -0.13  0.05 0.37 0.63 1.3
people.ought1      -0.05  0.22  0.51  0.06  0.02 -0.12 0.31 0.69 1.6
expect.ought1       0.03 -0.03  0.83  0.01 -0.01  0.01 0.70 0.30 1.0
fail.ought1         0.01  0.01  0.62 -0.09  0.10  0.05 0.39 0.61 1.1
enjoy.intr1         0.02 -0.05 -0.12  0.01  0.73 -0.02 0.55 0.45 1.1
life.intr1         -0.11  0.10  0.18  0.13  0.61  0.15 0.56 0.44 1.5
exciting.intr1      0.25  0.02 -0.01  0.18  0.38 -0.03 0.35 0.65 2.3
challenge.intr1     0.21 -0.10  0.00 -0.05  0.43  0.14 0.26 0.74 1.9
job.instru1        -0.01  0.78  0.06 -0.01 -0.07  0.05 0.58 0.42 1.0
knowledge.instru1   0.13 -0.02  0.11 -0.02  0.17  0.38 0.24 0.76 1.9
career.instru1      0.00  0.76 -0.06 -0.01  0.04 -0.02 0.59 0.41 1.0
money.instru1       0.01  0.52  0.07 -0.10  0.02  0.11 0.30 0.70 1.2
time.integr1        0.07  0.00 -0.08  0.63  0.10 -0.03 0.47 0.53 1.1
becomelike.integr1 -0.01 -0.08  0.11  0.43  0.04  0.22 0.27 0.73 1.7
meeting.integr1     0.05  0.03 -0.12  0.56  0.13 -0.08 0.41 0.59 1.3
affinity.integr1   -0.11 -0.05  0.09  0.72 -0.07  0.03 0.49 0.51 1.1
improve.prof1       0.70 -0.08 -0.03  0.09 -0.06  0.09 0.51 0.49 1.1
speaking.prof1      0.80  0.08 -0.04  0.10 -0.12 -0.01 0.65 0.35 1.1
reading.prof1       0.70 -0.04  0.01 -0.14  0.11 -0.04 0.51 0.49 1.1
written.prof1       0.76  0.09  0.05 -0.03  0.05 -0.10 0.61 0.39 1.1
listening.prof1     0.86 -0.07  0.05 -0.05  0.03  0.07 0.76 0.24 1.0
citizen.post1       0.05  0.21  0.09  0.03  0.05  0.52 0.43 0.57 1.4
interact.post1      0.01  0.32 -0.19  0.10  0.19  0.17 0.34 0.66 3.2
overseas.post1      0.29  0.27 -0.08  0.17 -0.02  0.25 0.36 0.64 3.8
globalaccess.post1  0.05  0.36 -0.19  0.11  0.16  0.34 0.50 0.50 3.2

                       MR2  MR4  MR3  MR5  MR1  MR6
SS loadings           3.35 2.47 1.88 2.11 2.15 1.03
Proportion Var        0.12 0.09 0.06 0.07 0.07 0.04
Cumulative Var        0.12 0.20 0.27 0.34 0.41 0.45
Proportion Explained  0.26 0.19 0.14 0.16 0.17 0.08
Cumulative Proportion 0.26 0.45 0.59 0.76 0.92 1.00

 With factor correlations of 
     MR2  MR4   MR3  MR5   MR1  MR6
MR2 1.00 0.13  0.05 0.11  0.22 0.16
MR4 0.13 1.00  0.00 0.33  0.37 0.24
MR3 0.05 0.00  1.00 0.03 -0.05 0.11
MR5 0.11 0.33  0.03 1.00  0.39 0.16
MR1 0.22 0.37 -0.05 0.39  1.00 0.16
MR6 0.16 0.24  0.11 0.16  0.16 1.00

Mean item complexity =  1.8
Test of the hypothesis that 6 factors are sufficient.

The degrees of freedom for the null model are  406  and the objective function was  10.52 with Chi Square of  3278.37
The degrees of freedom for the model are 247  and the objective function was  1.46 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic number of observations is  323 with the empirical chi square  293.67  with prob <  0.022 
The total number of observations was  323  with Likelihood Chi Square =  448.4  with prob <  7.6e-14 

Tucker Lewis Index of factoring reliability =  0.883
RMSEA index =  0.053  and the 90 % confidence intervals are  0.043 0.058
BIC =  -978.68
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   MR2  MR4  MR3  MR5
Correlation of (regression) scores with factors   0.95 0.91 0.90 0.88
Multiple R square of scores with factors          0.90 0.82 0.81 0.78
Minimum correlation of possible factor scores     0.80 0.65 0.63 0.55
                                                   MR1  MR6
Correlation of (regression) scores with factors   0.89 0.78
Multiple R square of scores with factors          0.79 0.61
Minimum correlation of possible factor scores     0.57 0.22

# plot loadings
loadings_basic <- fa_basic$loadings
class(loadings_basic)<-"matrix"
colnames(loadings_basic)<-paste("F",1:fact,sep="")
loadings_basic<-as.data.frame(loadings_basic)
loadings_basic<-round(loadings_basic,2)
loadings_basic$D <- rownames(loadings_basic)
a1 <- loadings_basic
a1 <- melt(a1,id.vars=c("D"))
a1$inv <- ifelse(a1$value < 0 ,"neg","pos")
a1$value[abs(a1$value) < loading_cutoff] <- 0
a1 <- a1[a1$value!=0,]
a1 <- a1 %>% separate(D,into = c("Variable","Item"),remove=FALSE,sep="[.]")
ggplot(a1)+geom_bar(aes(x=reorder(D, value) ,y=value,fill=Item),stat="identity")+facet_wrap(~variable,ncol = 2,scales = "free_y")+coord_flip() + geom_hline(yintercept = c(-0.3,0.3),linetype="dotted",colour="dark red")

# Table of the factors
loadings_basic$D <- NULL
loadings_basic[abs(loadings_basic) < loading_cutoff] <- 0
for(i in 1:ncol(loadings_basic)){loadings_basic[,i] <- as.character(loadings_basic[,i])}
loadings_basic[loadings_basic=="0"] <- ""
loading_fact_reduced <- loadings_basic
loading_fact_reduced

# predict values per samples
pred_basic <- as.data.frame(predict(fa_basic,usable_data))
names(pred_basic) <- paste("Factor",1:fact,sep = "")
factors <- names(pred_basic)
match_initial_data <- match(all$Resp.ID,rownames(pred_basic))
all_complete_basic <- cbind(all,scale(pred_basic[match_initial_data,]))
corrplot(cor(all_complete_basic[,usable_items],all_complete_basic[,factors],use = "pair"))

# Plot loadings by context
all_complete_basic <- melt(all_complete_basic,id.vars = "Context",measure.vars = factors)
library(ggplot2)
ggplot(all_complete_basic)+geom_boxplot(aes(x=Context,y=value,color=Context))+facet_wrap(~variable)+coord_flip()+guides(color=F)

# 7 * 12 rows removed
# error bar 
sum_stat <- all_complete_basic %>% group_by(Context,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(Context[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)
ggplot(sum_stat,aes(x=Context,y=meanFac,colour=Context)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2) + facet_wrap(~variable,scales="free_y") + geom_point() +theme(axis.text.x = element_text(angle = 45, hjust = 1))+ ggtitle("Mean +- 95% CI")

ggplot(sum_stat,aes(x=variable,y=meanFac,colour=variable)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2) + facet_wrap(~Context,scales="free_y") + 
  geom_point() + ggtitle("Mean +- 95% CI")

kable(sum_stat)

Context	variable	meanFac	stdFac	nObs	seMean	CI95
English in Germany	Factor1	-0.7673653	1.2968739	70	0.1550061	0.3038119
English in Germany	Factor2	0.2464654	0.8811501	70	0.1053176	0.2064224
English in Germany	Factor3	-0.4025772	0.6874385	70	0.0821646	0.1610427
English in Germany	Factor4	0.3070734	0.9509279	70	0.1136576	0.2227689
English in Germany	Factor5	0.0672303	0.8805028	70	0.1052402	0.2062708
English in Germany	Factor6	-0.3916784	1.0244232	70	0.1224420	0.2399863
English in Italy	Factor1	0.1674403	0.7825545	91	0.0820340	0.1607866
English in Italy	Factor2	0.5194919	0.7674261	91	0.0804481	0.1576783
English in Italy	Factor3	0.0054434	0.9238201	91	0.0968427	0.1898116
English in Italy	Factor4	0.0311704	0.9431596	91	0.0988700	0.1937852
English in Italy	Factor5	0.4084333	0.8766512	91	0.0918980	0.1801201
English in Italy	Factor6	0.3768171	0.8018947	91	0.0840614	0.1647604
German in Australia	Factor1	0.2302922	0.7943686	88	0.0846800	0.1659728
German in Australia	Factor2	-0.2004232	1.0176085	88	0.1084774	0.2126158
German in Australia	Factor3	0.0300804	1.1010277	88	0.1173699	0.2300451
German in Australia	Factor4	-0.2897234	1.1273569	88	0.1201766	0.2355462
German in Australia	Factor5	-0.3245639	1.0203688	88	0.1087717	0.2131925
German in Australia	Factor6	-0.0289222	1.0127781	88	0.1079625	0.2116065
Italian in Australia	Factor1	0.2461188	0.7676304	74	0.0892352	0.1749010
Italian in Australia	Factor2	-0.6336365	0.9310097	74	0.1082277	0.2121263
Italian in Australia	Factor3	0.3383511	1.0930484	74	0.1270643	0.2490460
Italian in Australia	Factor4	0.0157300	0.8670613	74	0.1007938	0.1975559
Italian in Australia	Factor5	-0.1798909	1.0572445	74	0.1229022	0.2408883
Italian in Australia	Factor6	-0.0584826	1.0369273	74	0.1205404	0.2362591

0.4 Factor analysis correcting for context

# items to be used for the FA
usable_items <- likert_variables1[!(likert_variables1 %in% c("necessity1","educated1","reconnect.comm1", "speakersmelb.comm1", "comecloser.comm1"))]
usable_data <- all[,c(usable_items,"Context")]
dat_onlyItems <- usable_data[,usable_items]
# get residuals after regressing for context
get_residuals <- function(item,pred = dat$Context){
  mod <- lm(item ~ pred)
  return(mod$residuals)
}
applygetRes <- apply(as.matrix(dat_onlyItems),2,get_residuals,
                     pred=usable_data$Context)
# Factanal 
# From a statisticak point of view 
fap <- fa.parallel(applygetRes)

Parallel analysis suggests that the number of factors =  6  and the number of components =  6 

fact <- 6
loading_cutoff <- 0.2
fa_basic <- fa(applygetRes,fact)
fa_basic

Factor Analysis using method =  minres
Call: fa(r = applygetRes, nfactors = fact)
Standardized loadings (pattern matrix) based upon correlation matrix
                     MR2   MR1   MR3   MR4   MR5   MR6   h2   u2 com
converse.id1        0.06  0.45  0.04  0.12  0.14  0.09 0.39 0.61 1.5
dream.id1           0.16  0.29  0.04  0.23  0.21 -0.28 0.37 0.63 4.4
usewell.id1         0.08  0.15  0.04  0.21  0.25 -0.10 0.22 0.78 3.4
whenever.id1        0.01  0.23  0.09  0.21  0.34 -0.02 0.36 0.64 2.7
consider.ought1     0.08  0.02  0.56  0.04 -0.10  0.10 0.36 0.64 1.2
people.ought1       0.01  0.03  0.53  0.17 -0.01 -0.09 0.32 0.68 1.3
expect.ought1       0.00  0.02  0.82 -0.02 -0.01  0.00 0.67 0.33 1.0
fail.ought1         0.00 -0.03  0.62 -0.04  0.06  0.01 0.39 0.61 1.0
enjoy.intr1         0.02  0.00 -0.11 -0.02  0.75 -0.02 0.57 0.43 1.0
life.intr1         -0.09  0.18  0.18  0.07  0.55  0.12 0.51 0.49 1.7
exciting.intr1      0.17  0.21 -0.02  0.08  0.39 -0.07 0.37 0.63 2.1
challenge.intr1     0.17 -0.08 -0.01 -0.05  0.46  0.15 0.28 0.72 1.6
job.instru1         0.00 -0.04  0.06  0.78 -0.05  0.05 0.60 0.40 1.0
knowledge.instru1   0.03 -0.02  0.06  0.06  0.21  0.38 0.25 0.75 1.7
career.instru1     -0.01  0.03 -0.07  0.72  0.03 -0.04 0.53 0.47 1.0
money.instru1      -0.01 -0.14  0.07  0.54  0.07  0.12 0.33 0.67 1.3
time.integr1        0.04  0.64 -0.05 -0.01  0.09 -0.02 0.47 0.53 1.1
becomelike.integr1  0.00  0.38  0.11 -0.06  0.05  0.25 0.26 0.74 2.1
meeting.integr1     0.07  0.55 -0.09 -0.01  0.10 -0.06 0.38 0.62 1.2
affinity.integr1   -0.09  0.67  0.11 -0.05 -0.06  0.07 0.44 0.56 1.1
improve.prof1       0.64  0.14 -0.06 -0.04 -0.07  0.06 0.44 0.56 1.2
speaking.prof1      0.73  0.13 -0.07  0.12 -0.13 -0.04 0.60 0.40 1.2
reading.prof1       0.69 -0.13  0.01 -0.08  0.10 -0.01 0.48 0.52 1.1
written.prof1       0.78 -0.05  0.08  0.04  0.05 -0.05 0.62 0.38 1.1
listening.prof1     0.83 -0.04  0.03 -0.06  0.04  0.06 0.69 0.31 1.0
citizen.post1       0.05  0.06  0.07  0.13  0.00  0.54 0.40 0.60 1.2
interact.post1      0.09  0.21 -0.17  0.14  0.12  0.19 0.25 0.75 4.9
overseas.post1      0.29  0.20 -0.06  0.18 -0.03  0.27 0.35 0.65 3.6
globalaccess.post1  0.05  0.15 -0.19  0.29  0.15  0.35 0.46 0.54 3.5

                       MR2  MR1  MR3  MR4  MR5  MR6
SS loadings           3.08 2.28 1.87 2.07 1.99 1.07
Proportion Var        0.11 0.08 0.06 0.07 0.07 0.04
Cumulative Var        0.11 0.19 0.25 0.32 0.39 0.43
Proportion Explained  0.25 0.18 0.15 0.17 0.16 0.09
Cumulative Proportion 0.25 0.43 0.59 0.75 0.91 1.00

 With factor correlations of 
      MR2  MR1   MR3  MR4   MR5  MR6
MR2  1.00 0.20 -0.04 0.23  0.27 0.11
MR1  0.20 1.00  0.05 0.35  0.40 0.20
MR3 -0.04 0.05  1.00 0.08 -0.04 0.12
MR4  0.23 0.35  0.08 1.00  0.30 0.27
MR5  0.27 0.40 -0.04 0.30  1.00 0.16
MR6  0.11 0.20  0.12 0.27  0.16 1.00

Mean item complexity =  1.8
Test of the hypothesis that 6 factors are sufficient.

The degrees of freedom for the null model are  406  and the objective function was  9.64 with Chi Square of  3002.9
The degrees of freedom for the model are 247  and the objective function was  1.41 

The root mean square of the residuals (RMSR) is  0.03 
The df corrected root mean square of the residuals is  0.04 

The harmonic number of observations is  323 with the empirical chi square  304.9  with prob <  0.007 
The total number of observations was  323  with Likelihood Chi Square =  433.55  with prob <  2.2e-12 

Tucker Lewis Index of factoring reliability =  0.88
RMSEA index =  0.051  and the 90 % confidence intervals are  0.041 0.056
BIC =  -993.53
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy             
                                                   MR2  MR1 MR3  MR4
Correlation of (regression) scores with factors   0.94 0.88 0.9 0.89
Multiple R square of scores with factors          0.88 0.78 0.8 0.80
Minimum correlation of possible factor scores     0.76 0.56 0.6 0.60
                                                   MR5  MR6
Correlation of (regression) scores with factors   0.88 0.78
Multiple R square of scores with factors          0.77 0.61
Minimum correlation of possible factor scores     0.54 0.22

# plot loadings
loadings_basic <- fa_basic$loadings
class(loadings_basic)<-"matrix"
colnames(loadings_basic)<-paste("F",1:fact,sep="")
loadings_basic<-as.data.frame(loadings_basic)
loadings_basic<-round(loadings_basic,2)
loadings_basic$D <- rownames(loadings_basic)
a1 <- loadings_basic
a1 <- melt(a1,id.vars=c("D"))
a1$inv <- ifelse(a1$value < 0 ,"neg","pos")
a1$value[abs(a1$value) < loading_cutoff] <- 0
a1 <- a1[a1$value!=0,]
a1 <- a1 %>% separate(D,into = c("Variable","Item"),remove=FALSE,sep="[.]")
ggplot(a1)+geom_bar(aes(x=reorder(D, value) ,y=value,fill=Item),stat="identity")+facet_wrap(~variable,ncol = 2,scales = "free_y")+coord_flip() + geom_hline(yintercept = c(-0.3,0.3),linetype="dotted",colour="dark red")

# Table of the factors
loadings_basic$D <- NULL
loadings_basic[abs(loadings_basic) < loading_cutoff] <- 0
for(i in 1:ncol(loadings_basic)){loadings_basic[,i] <- as.character(loadings_basic[,i])}
loadings_basic[loadings_basic=="0"] <- ""
loading_fact_reduced <- loadings_basic
loading_fact_reduced

# predict values per samples
pred_basic <- as.data.frame(predict(fa_basic,dat_onlyItems))
names(pred_basic) <- paste("Factor",1:fact,sep = "")
factors <- names(pred_basic)
match_initial_data <- match(all$Resp.ID,rownames(pred_basic))
all_complete_basic <- cbind(all,scale(pred_basic[match_initial_data,]))
corrplot(cor(all_complete_basic[,usable_items],all_complete_basic[,factors],use = "pair"))

# Plot loadings by context
all_complete_melt <- melt(all_complete_basic,id.vars = "Context",measure.vars = factors)
library(ggplot2)
ggplot(all_complete_melt)+geom_boxplot(aes(x=Context,y=value,color=Context))+facet_wrap(~variable)+coord_flip()+guides(color=F)

# error bar 
sum_stat <- all_complete_melt %>% group_by(Context,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(Context[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)
ggplot(sum_stat,aes(x=Context,y=meanFac,colour=Context)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2) + facet_wrap(~variable,scales="free_y") + geom_point() +theme(axis.text.x = element_text(angle = 45, hjust = 1))+ ggtitle("Mean +- 95% CI")

ggplot(sum_stat,aes(x=variable,y=meanFac,colour=variable)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2) + facet_wrap(~Context,scales="free_y") + 
  geom_point() + ggtitle("Mean +- 95% CI")

kable(sum_stat)

Context	variable	meanFac	stdFac	nObs	seMean	CI95
English in Germany	Factor1	-0.7262823	1.3027239	70	0.1557053	0.3051824
English in Germany	Factor2	0.2482873	0.9717385	70	0.1161450	0.2276441
English in Germany	Factor3	-0.3577921	0.6873827	70	0.0821579	0.1610296
English in Germany	Factor4	0.1984720	0.9209535	70	0.1100750	0.2157470
English in Germany	Factor5	0.0623044	0.8805362	70	0.1052442	0.2062786
English in Germany	Factor6	-0.2942834	1.0170296	70	0.1215583	0.2382543
English in Italy	Factor1	0.1843902	0.7928113	91	0.0831092	0.1628940
English in Italy	Factor2	0.1305766	0.9120258	91	0.0956063	0.1873883
English in Italy	Factor3	0.0131736	0.9281411	91	0.0972956	0.1906994
English in Italy	Factor4	0.4605985	0.8027893	91	0.0841552	0.1649442
English in Italy	Factor5	0.3597625	0.8859079	91	0.0928684	0.1820220
English in Italy	Factor6	0.3618400	0.8155681	91	0.0854948	0.1675697
German in Australia	Factor1	0.2071940	0.8075060	88	0.0860804	0.1687176
German in Australia	Factor2	-0.3001195	1.1310092	88	0.1205660	0.2363093
German in Australia	Factor3	0.0073308	1.1099903	88	0.1183254	0.2319177
German in Australia	Factor4	-0.1437635	1.0280115	88	0.1095864	0.2147893
German in Australia	Factor5	-0.2915304	1.0361113	88	0.1104498	0.2164817
German in Australia	Factor6	-0.0633571	1.0120855	88	0.1078887	0.2114618
Italian in Australia	Factor1	0.2138808	0.7800659	74	0.0906808	0.1777344
Italian in Australia	Factor2	-0.0385415	0.8820267	74	0.1025335	0.2009657
Italian in Australia	Factor3	0.3135343	1.1005654	74	0.1279381	0.2507587
Italian in Australia	Factor4	-0.5831934	0.9398504	74	0.1092554	0.2141406
Italian in Australia	Factor5	-0.1546625	1.0673902	74	0.1240816	0.2431999
Italian in Australia	Factor6	-0.0912455	1.0643970	74	0.1237336	0.2425179

0.5 Demographics

demographics_var <- c("Age","Gender","L1","speak.other.L2","study.other.L2","origins","year.studyL2","other5.other.ways","degree","roleL2.degree","study.year","prof","L2.VCE","uni1.year","Context")
dat_fac_demo <- all_complete_basic[,c(demographics_var,factors)]
table(dat_fac_demo$Age) 

18-25 26-30 31-35 
  318     4     1 

table(dat_fac_demo$L1) # to be changed

         Afrikaans           Albanian          Cantonese 
                 1                  1                  2 
           Chinese              Dutch            English 
                 4                  1                147 
 English and Dutch             German German and English 
                 2                 63                  2 
                 I         Indonesian            Italian 
                 1                  1                 87 
          Japanese           Mandarin    Persian (Farsi) 
                 1                  2                  1 
          Romanian            Russian             Sindhi 
                 1                  2                  1 
           Spanish            Turkish          Ukrainian 
                 1                  1                  1 

table(dat_fac_demo$speak.other.L2) # to be changed

                                                             Afrikaans 
                                                                     1 
                                                                Arabic 
                                                                     1 
                                            Azeri, Turkish and English 
                                                                     1 
                                                               Chinese 
                                                                     1 
                                                   Chinese (Cantonese) 
                                                                     1 
                                                    Dutch (and German) 
                                                                     1 
                                                               English 
                                                                     5 
                                                     English\nJapanese 
                                                                     1 
                                                     English, Javanese 
                                                                     1 
                                                     English, Mandarin 
                                                                     1 
                                                                French 
                                                                    10 
                                           French and learning Spanish 
                                                                     1 
                                                        French, Greek. 
                                                                     1 
               French, not fluent, but have a fair amount of knowledge 
                                                                     1 
                                                               French. 
                                                                     1 
                                                                German 
                                                                     1 
                                    German (proficient/advanced level) 
                                                                     1 
                                                   German and Japanese 
                                                                     1 
                                                        German, French 
                                                                     1 
                                                               German. 
                                                                     1 
                                                                 Greek 
                                                                     2 
                                                                 Hindi 
                                                                     1 
                                                            Indonesian 
                                                                     1 
Indonesian and French (not fluent in either, but did VCE both of them) 
                                                                     1 
                                                                 Irish 
                                                                     1 
                                                               Italian 
                                                                     5 
                                                              Japanese 
                                                                     1 
                                                            Macedonian 
                                                                     1 
                                                                    No 
                                                                   141 
                                                           Only German 
                                                                     1 
                                                                Polish 
                                                                     1 
                                                               Russian 
                                                                     1 
                                                               Serbian 
                                                                     1 
                                                          Some Italian 
                                                                     1 
                                                               Spanish 
                                                                     2 
                                                               Swedish 
                                                                     1 
                                                                Telugu 
                                                                     1 
                                                         Urdu, English 
                                                                     1 
                                                                   Yes 
                                                                   124 

table(dat_fac_demo$study.other.L2) # to be changed

                                                                            Ancient Greek 
                                                                                        1 
                                                                                     Arab 
                                                                                        1 
                                                                                  Arabian 
                                                                                        1 
                                                                                   Arabic 
                                                                                        2 
                                                                                    Arabo 
                                                                                        1 
                                                                                  Chinese 
                                                                                        7 
                                                                                  CHINESE 
                                                                                        1 
                                                                       Chinese (Mandarin) 
                                                                                        1 
                                                                         Chinese mandarin 
                                                                                        1 
                                                                                 Chinese. 
                                                                                        1 
                                                                                    Dutch 
                                                                                        2 
                                                                                  Finnish 
                                                                                        1 
                                                                                 Francese 
                                                                                        1 
                                                                                   French 
                                                                                       19 
                                                       French (5 semesters) until 07/2016 
                                                                                        1 
                                                                       french and spanish 
                                                                                        2 
                                                                       French and Spanish 
                                                                                        1 
                                                                           French, Greek. 
                                                                                        1 
                                                                           French,Spanish 
                                                                                        1 
                                                                                  French. 
                                                                                        2 
                                                                                   German 
                                                                                        9 
                                                 I also study French at university level. 
                                                                                        1 
I am also learning Spanish at University, although only at beginner level, unlike German. 
                                                                                        1 
                   I study Russian, I plan to learn Spanish and hopefully also Portuguese 
                                                                                        1 
                   I'm studying German. Since I've never studied it before, I a beginner. 
                                                                                        1 
                                                                                  Italian 
                                                                                        5 
                                                                                 japanese 
                                                                                        1 
                                                                                 Japanese 
                                                                                       13 
                                                                 Japanese (very beginner) 
                                                                                        1 
                                       Japanese but I'm not going to continue learning it 
                                                                                        1 
                                                                                Japanese. 
                                                                                        1 
                                                                                    Latin 
                                                                                        1 
                                                  Latin, Ancient Egyptian, Ancient Greek. 
                                                                                        1 
                                                             Latin, doesn't really count. 
                                                                                        1 
                                                                              Netherlands 
                                                                                        1 
                                                                                       No 
                                                                                      179 
                                                                         Nonna da Pescara 
                                                                                        1 
                                                                                   Polish 
                                                                                        2 
                                                                               Portoghese 
                                                                                        1 
                                                                                Portugese 
                                                                                        1 
                                                                               Portuguese 
                                                                                        2 
                                                                                  Russian 
                                                                                       15 
                                                                                 Russian. 
                                                                                        1 
                                                                                    russo 
                                                                                        1 
                                                                                    Russo 
                                                                                        2 
                                                                               siehe oben 
                                                                                        1 
                                                                                 Spagnolo 
                                                                                        2 
                                                          Spagnolo e un po' di giapponese 
                                                                                        1 
                                                                                  Spanish 
                                                                                       16 
                                                                              Spanish (1) 
                                                                                        1 
                                                                                 Spanish. 
                                                                                        2 
                                                                                  tedesco 
                                                                                        1 
                                                                                  Tedesco 
                                                                                        5 
                                                        Will start my French diploma soon 
                                                                                        1 

table(dat_fac_demo$origins)

 No Yes 
254  69 

table(dat_fac_demo$year.studyL2) # to be changed

                     0 years                   1- 3 years 
                          33                            9 
                   1-3 years                    4-6 years 
                           7                           53 
                   BILINGUAL First year of primary school 
                           4                           73 
        FIRST.YEAR.SECONDARY          FOURTH.YEAR.PRIMARY 
                          10                            5 
                Kindergarten             Less than a year 
                          29                           18 
             LOWER.SECONDARY            more than 6 years 
                           4                           41 
                    PERSONAL          SECOND.YEAR.PRIMARY 
                           2                            2 
       SECOND.YEAR.SECONDARY           THIRD.YEAR.PRIMARY 
                           2                           28 

table(dat_fac_demo$other5.other.ways) # to be changed

                     COURSE               COURSE; MEDIA 
                          5                           1 
                   EXCHANGE                     FRIENDS 
                          6                           4 
                   HERITAGE                L2.RESOURCES 
                          4                          19 
        L2.RESOURCES, MEDIA         L2.RESOURCES; MEDIA 
                          1                           1 
                  LIVING.L2           M.PRIVATE.LESSONS 
                          7                           2 
              NO.OTHER.WAYS               ONLINE.COURSE 
                          1                           4 
                   PERSONAL           PERSONAL.HERITAGE 
                          3                           2 
                         QC                  SELF.STUDY 
                          1                           7 
              STUDY.HOLIDAY TRAVEL.FRIENDS.L2.RESOURCES 
                          5                           1 
                 TRAVELLING                     WORK.L2 
                          8                           2 

table(dat_fac_demo$degree) # to be changed

                    BA in Anglistik            BA in Nordamerikastudien 
                                 39                                   4 
                                HUM                             HUM.SCI 
                                 97                                   5 
                                 LA      Lingue e letterature straniere 
                                 27                                  78 
Lingue, mercati e culture dell'Asia                                  QC 
                                 13                                   4 
                                SCI 
                                 56 

table(dat_fac_demo$roleL2.degree) # not usable

First or second language 
                      91 

table(dat_fac_demo$study.year)

1st semester     1st year 
          70          253 

table(dat_fac_demo$prof)

          Advanced         Elementary       Intermediate 
                65                 63                 68 
Upper-intermediate 
               127 

table(dat_fac_demo$L2.VCE)

 No Yes 
 47  90 

table(dat_fac_demo$uni1.year) # not usable

1st year 
     162 

demo_melt <- melt(all_complete_basic,id.vars = c("Age","Gender","origins","study.year","prof","L2.VCE","Context"),measure.vars = factors)
# age
ageStat <- demo_melt %>% group_by(Context,Age,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(Age[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)
ageStat$Demo <- "Age"
colnames(ageStat)[2] <- "levels"
ageStat <- data.frame(ageStat)
# Gender
GenderStat <- demo_melt %>% group_by(Context,Gender,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(Gender[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)
GenderStat$Demo <- "Gender"
colnames(GenderStat)[2] <- "levels"
GenderStat <- data.frame(GenderStat)
# origins
originsStat <- demo_melt %>% group_by(Context,origins,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(origins[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)
originsStat$Demo <- "origins"
colnames(originsStat)[2] <- "levels"
originsStat <- data.frame(originsStat)
# study.year
study.yearStat <- demo_melt %>% group_by(Context,study.year,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(study.year[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)
study.yearStat$Demo <- "Study Year"
colnames(study.yearStat)[2] <- "levels"
study.yearStat <- data.frame(study.yearStat)
# prof
profStat <- demo_melt %>% group_by(Context,prof,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(prof[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)
profStat$Demo <- "Proficiency"
colnames(profStat)[2] <- "levels"
profStat$levels <- as.character(profStat$levels)
profStat <- data.frame(profStat)
# L2.VCE
L2.VCEStat <- demo_melt %>% group_by(Context,L2.VCE,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(L2.VCE[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)
L2.VCEStat$Demo <- "L2.VCE"
colnames(L2.VCEStat)[2] <- "levels"
L2.VCEStat$levels <- as.character(L2.VCEStat$levels)
L2.VCEStat <- data.frame(L2.VCEStat)
##################
# Combine stats
##################
combine_stat <- rbind(data.frame(L2.VCEStat),data.frame(profStat),study.yearStat,originsStat,ageStat,GenderStat)

0.5.1 Tables

• Age

kable(ageStat)

• Gender

kable(GenderStat)

• origins

kable(originsStat)

• study.year

kable(study.yearStat)

• prof

kable(profStat)

• L2.VCE

kable(L2.VCEStat)

0.5.2 Factor means with Confidence Intervals

pos <- position_dodge(width=0.4)
ggplot(subset(combine_stat,variable %in% c("Factor1")),aes(x=levels,y=meanFac,colour=Context,group=Context)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2,position=pos) + facet_wrap(~Demo ,scales="free") +
  geom_point(position=pos) + ggtitle("Factor1: Mean +- 95% CI") + theme_bw()

pos <- position_dodge(width=0.4)
ggplot(subset(combine_stat,variable %in% c("Factor2")),aes(x=levels,y=meanFac,colour=Context,group=Context)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2,position=pos) + facet_wrap(~Demo ,scales="free") +
  geom_point(position=pos) + ggtitle("Factor2: Mean +- 95% CI") + theme_bw()

pos <- position_dodge(width=0.4)
ggplot(subset(combine_stat,variable %in% c("Factor3")),aes(x=levels,y=meanFac,colour=Context,group=Context)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2,position=pos) + facet_wrap(~Demo ,scales="free") +
  geom_point(position=pos) + ggtitle("Factor3: Mean +- 95% CI") + theme_bw()

pos <- position_dodge(width=0.4)
ggplot(subset(combine_stat,variable %in% c("Factor4")),aes(x=levels,y=meanFac,colour=Context,group=Context)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2,position=pos) + facet_wrap(~Demo ,scales="free") +
  geom_point(position=pos) + ggtitle("Factor4: Mean +- 95% CI") + theme_bw()


pos <- position_dodge(width=0.4)
ggplot(subset(combine_stat,variable %in% c("Factor5")),aes(x=levels,y=meanFac,colour=Context,group=Context)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2,position=pos) + facet_wrap(~Demo ,scales="free") +
  geom_point(position=pos) + ggtitle("Factor5: Mean +- 95% CI") + theme_bw()

pos <- position_dodge(width=0.4)
ggplot(subset(combine_stat,variable %in% c("Factor6")),aes(x=levels,y=meanFac,colour=Context,group=Context)) + 
geom_errorbar(aes(ymin=meanFac-CI95, ymax=meanFac+CI95),width=0.2,position=pos) + facet_wrap(~Demo ,scales="free") +
  geom_point(position=pos) + ggtitle("Factor6: Mean +- 95% CI") + theme_bw()

1 Degree (HUM vs STEMM)

We could probably reduce the number of classes.

# L2.VCE
degreeStat <- degree_melt %>% group_by(Context,degree,variable) %>%
  summarise(meanFac = mean(value,na.rm=TRUE),
            stdFac = sd(value,na.rm=TRUE),
            nObs = length(L2.VCE[!is.na(value)])) %>%
  mutate(seMean = stdFac/sqrt(nObs),
         CI95 = 1.96*seMean)

Error in summarise_impl(.data, dots) : 
  Evaluation error: object 'L2.VCE' not found.